Python Programming and Statistics

Question

In the winter season in the United States it is estimated that 30% of the population contracts respiratory diseases. If a sample of 350 people is taken, using Normal approximation to the binomial

a) The probability that more than 150 of them will eventually contract some kind of respiratory diseases ?.

b) The probability that between 25 percent and 35 percent of patients contract some type of respiratory disease.

c) If a large number of people, say N, get respiratory disease then the city will be declared in emergency. What this N value should be if you want the city to be declared in emergency only 5% of the time.

Answer 1

mean = 350 * 0.3 = 105

std dev = sqrt( 350 * 0.3 * 0.7) = 8.573214

a) Prob( x> 150 ) = 1 - prob ( x < 150) = 1 - (z< (150-105)/8.573214)) = 0

b) 350(0.25) = 87.5 and 350*0.35 = 122.5

Prob ( 87.5 < x < 122.5) = Prob ( x < 122.5) - Prob(87.5) = 0.958773 <--- must convert to z-scores first

c) Based on the result of (b) , about N=120